Question

Can someone explain me what is \(\color{green}{Rank}\) of a Matrix and how to find it?

Answer 1

the rank of a matrix is the number of linearly independent rows

Answer 2

Start from the start..

What is now this Linearly Independent Rows??

Can you make it simple for me to understand, by not going deeper..

Answer 3

The matrix rank is determined by the number of ''independent rows or columns'' present in it. A row or a column is considered independent, if it satisfies the below conditions:
1. A row should have atleast one non-zero element .
2. A row should not be identical to another row.
3. A row should not be proportional (multiples) of another row.
4. A row should not be should not be a linear combination of another row.

For finding the rank of a matrix , first convert it into Echelon Form...

Answer 4

You are giving me written things, I am saying to explain it and to make me understand in simpler way..

Answer 5

Probably this would help you ...
If you feel you have some elementary ideas of a matrix, let's take an example... would it be okay???

Answer 6

Okay, by taking examples things go easy..

Answer 7

Take, for example the matrix,
Since the 1st element is non zero (and specially 1), we do not need to make any transformation for that...
Now, in order to change it into Echelon Form, we need to convert it into upper triangular or lower triangular matrix, okay???